It is known that to diagnose and treat bone pathologies, such as for example osteoporosis, it is first of all necessary to evaluate the mechanical properties, particularly elasticity and resistance to applied loads.
In order to estimate the resistance and elasticity of the bone with a good level of accuracy, however, it is not enough to know its composition and density. The elastic properties of the bone tissue depend to a large extent on the architecture of the bone structure in the sample in question, as is known, for example, from: Martin, R. B. (1991) J. Biomech., 24, 79-88, and from: Waud, C. E. et al. (1992) Calcif. Tissue Int., 51, 416-418; and mechanical resistance is linearly proportionate to the value of Young modulus [Hodgkinson, R. J., Currey, D. (1990) P.I.M.E., 204, 115-121]. At present, the mechanical properties of the bones, and in particular the parameters related to elasticity and strength, cannot be determined by mechanical tests performed on the patient. Nor, for obvious reasons, is it appropriate to use bone samples taken from the patient on which the tests are to be performed in machines suitable for mechanical characterization. On the other hand, techniques for processing medical images have become very accurate, making it possible to perform digital modelling of the bone structure on different levels of definition, up to the range of some tenths of a micron.
The numerical methods at present employed for modelling and simulating the behavior of the bone structure for the purposes of estimating the mechanical properties have recourse to implementations of the finite elements method, known for example from Homminga, J. et al. (2001) J. Biomech., 34, 513-517.
This method, however, has the disadvantage that it does not allow to discretize the image easily, that is, to create a set of geometrical elements able to reproduce the structure examined as faithfully as possible and on which it is then possible to perform processing and elementary quantifications.
This operation, moreover, is long and laborious, to a large extent entrusted to the ability and experience of an operator, since the set of geometric elements has to be adapted to the conformation and irregularities of the bone structure examined.
Another application of the finite elements method provides to make a geometric element correspond to every voxel, or elementary volumetric unit, of the image acquired; however, this solution has the disadvantage that there is a very high number of elements present, such that processing the numeric model generated requires the use of computer networks which are not available in normal centers of analysis.
If the resolution, that is, the degree of detail, of the image is diminished in order to reduce the number of elements, the validity of the solution obtained inevitably declines.
In the case of identification of the bone micro-structure, another application of the finite elements method provides to use, as finite elements, rods of different length and section, constrained together so as to reproduce the trabecular structure.
This type of modeling generates, on the one hand, a number of unknowns low enough to be processed without particular strategies, but, on the other hand, the result obtained is not accurate enough.
The present Applicant has devised and embodied this invention to overcome these shortcomings of the state of the art, and to obtain other advantages.